The most straightforward way for the study of the dynamical evolution of the spin configurations of a ferromagnetic system consists in the use of Monte Carlo simulations [1]}. A Metropolis algorithm can be used in order to simulate the full evolution of the spin field, while the equilibrium state of the model described in the previous paragraph was studied in Ref. [2]} using Wolff's algorithm. For each Monte Carlo step, one random spin in a position \(\vec{r}=i,j,(k)\)  is chosen and flipped with probability \(P_{\vec{r}}\) , such that
\(P_{\vec{r}}= \left\lbrace  \begin{array}{lcc}e^{-\Delta E_{\vec{r}}/k_B T} & {\rm if} & \Delta E_{i,j,(k)} > 0, \\\\ 1/2 & {\rm if} & \Delta E_{i,j,(k)} = 0, \\\\ 1 & {\rm if} & \Delta E_{i,j,(k)} < 0,\end{array}\right.\) 
